# Math Help - Probability

1. ## Probability

Hi

The question is as follows:

An aircraft has three engines. Each engine can fail with the probability of 10^-4. Suppose that all three engines operate independently of each other. What is the probability that all engines fail? What is the probability that at least two engines fail at any given time?

2. so this would be a geometric probability distribution. so we have the probability of a failure being $10^{-4}$, therefore the probability of a success is $1-10^{-4}$

so the probability of a failure would be:

$P(X=3) = (10^{-4})(10^{-4})(10^{-4})=(10^{-4})^3 =10^{-12}$

for the second one, we would have:

$P(X \geq 2) = P(X \geq 2) \cup P(X=3) = (10^{-4})(10^{-4})(1-10^{-4})+(10^{-12})$ = $(10^{-4})^2(1-10^{-4}) +(10^{-12})$

3. $P(X \geq 2) = P(X {\color{red}=} 2) {\color{red}+} P(X=3) = ?$